A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two airplanes are separated by an angle of 58°. The large plane is 5.2km from the observation tower. a. Draw a diagram to represent this situation. b. How far is the small plane from the observation tower, to the nearest tenth of a kilometer?
Answers
Answer:
7.9km
Step-by-step explanation:
(a)See attached for the diagram representing this situation.
(b)
In Triangle ABC
[tex]\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ[/tex]
Next, we determine the value of Angle B.
[tex]\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ[/tex]
Finally, we find b.
[tex]\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)[/tex]
The distance between the small plane and the observation tower is 7.9km.
Related Questions
The sum of x and y is 7. The value of y is three more than the value of x. Write a system of equations to model this.
Answers
Answer:
x+y=7
y= x+3
Step-by-step explanation:
i just took the test
The system of the equation that represents the given condition will be x + y = 7 and y = x + 3. And the solution is (2, 5).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The sum of x and y is 7. The value of y is three more than the value of x. Then the equation is given as,
x + y = 7 ...1
y = x + 3 ...2
From equations 1 and 2, then we have
x + x + 3 = 7
2x = 4
x = 2
Then the value of the variable 'y' will be given as,
y = 2 + 3
y = 5
The system of the equation that represents the given condition will be x + y = 7 and y = x + 3. And the solution is (2, 5).
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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Write this number using standard notation,
1.5 x 10 to the 6th power
Type the correct answer, then press Enter.
Answers
Hey there! :)
Answer:
1,500,000.
Step-by-step explanation:
Convert to standard notation by first deriving the value of 10 to the exponent given:
[tex]10^{6} = 1,000,000[/tex] (6 zeros)
Multiply:
1.5 × 1,000,000 = 1,500,000
Set up the problem, but use a calculator to find the number of outcomes for the permutation. Eight horses run a race. In how many ways can the first three finishers turn out?
Answers
Explanation:
Label the slots A,B,C for first through third place.
There are 8 choices for slot A, 7 for slot B, and 6 for slot C. We start with 8 and count our way down until we get to the final slot. Then we multiply out those values
8*7*6 = 336
There are 336 ways to select three people from a pool of eight overall.
-----------------
If you want to use the permutation formula, then your steps might look like this
[tex]_n P _r = \frac{n!}{(n-r)!}\\\\_8 P _3 = \frac{8!}{(8-3)!}\\\\_8 P _3 = \frac{8!}{5!}\\\\_8 P _3 = \frac{8*7*6*5!}{5!}\\\\_8 P _3 = 8*7*6\\\\_8 P _3 = 336\\\\[/tex]
Note how the 5! terms cancel out on the second to last step, leaving behind the expression 8*7*6 which was found earlier.
local maximum of y=2x3+x2−7x−6.
Answers
Answer:
I did as linear equation hope it helps
Which symbol would make the statement TRUE?
4.589 4.958
A. <
B. >
C. =
D. none of the above
Answers
Answer:
A. <
Step-by-step explanation:
The symbol "<" means less than.
Comparing 4.589 with 4.958, 4.958 is greater than 4.589 by 0.369 (4.958 - 4.589).
So therefore, if we are to write 1 statement for both, we would say "4.589 is less than 4.958".
This can be written by using just symbols without words, thus, we have:
4.589 < 4.958.
The correct option is A. <
What is the range of this function?
Answers
Explanation: the range is the set of all possible resulting values of the dependent variable ( y )
A car is traveling at a rate of 100 kilometers per hour. What is the car's rate in miles per hour? How many miles will the car travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answers
Answer:
62mph
Step-by-step explanation:
Answer: 250 miles
Step-by-step explanation:
100 kph = 62.5 mph
In 4 hours, the car will travel
62.5 x 4 = 250 miles
Please help help❤️help me it would mean a lot
Answers
Answer:
B. points C, F and G
Step-by-step explanation:
B. Points G C F
10. Julio is driving to the store. The average distance d, in miles, he travels over t minutes is given by the
function d(t) = 0.5t. What is the value of the function when t = 15?
Answers
Answer:
7.5 miles
Step-by-step explanation:
Given the equation d(t) = 0.5t, all you need to do is plug in the value of t.
They're asking what the Function equals, and they're giving you the value of the variable t.
To solve, write the equation d(15) = 0.5(15)
And if you simplify the right side of the equation, you'll find that
d(15) = 7.5
If t represents time, then you can conclude that Julio travels 7.5 miles in the time t, of 15 minutes.
Three-fifths of the members of the Spanish club are girls. There are a total of 30 girls in the Spanish club.
Which statements can be used to solve for x, the total number of members in the Spanish club? Select three options
Answers
Problem: You do not have an attached picture. Though, I can help you out with this question.
So, three-fifths of the members are girls. There are 30 of girls. We can immediately make an equation using "x".
3/5x=30
3/5x × 5/3=30 × 5/3
x=50
Thus, there are 50 members in total. Though if x is too hard for you, you may substitute it by using another variable.
Variable in here is x.
Which of the following choices is the x intercept of the equation 2y-x=-6
Answers
Answer:
[tex]x = 6[/tex]
Step-by-step explanation:
Given
[tex]2y-x=-6[/tex]
Required
Determine the x intercept
To get the value of x intercept; we simply substitute 0 for y;
i.e. y = 0
[tex]2y-x=-6[/tex] becomes
[tex]2(0)-x=-6[/tex]
[tex]0-x=-6[/tex]
[tex]-x=-6[/tex]
Multiply both sides by -1
[tex]-1 * -x=-6 * -1[/tex]
[tex]x=-6 * -1[/tex]
[tex]x = 6[/tex]
Hence, the x intercept is 6
What else would need to be congruent to show that ABC= A DEF by SAS?
B
E
Given:
AC DF
ZCZE
А
O A. BC = EF
O B. ZCEF
O C. ZAŁ ZD
O D. AC = DF
Answers
Answer:
A.
Step-by-step explanation:
BC ≅ EF
BC needs to be congruent to EF to show that ΔABC ≅ ΔDEF by SAS(Side -Angle-Side) Postulate.
A student walk 60m on a bearing of 028 degree and then 180m due east. How is she from her starting point, correct to the nearest whole number?
Answers
Answer: she is 215m from her starting point
Step-by-step explanation:
The diagram representing the situation is shown in the attached photo. Triangle ABC is formed with AC representing her distance from her starting point.
Angle B = 28 + 90 = 118°
To determine AC, we would apply the law of Cosines which is expressed as
a² = b² + c² - 2abCosA
Where a,b and c are the length of each side of the triangle and B is the angle corresponding to b(AC). Likening the expression to the given triangle, it becomes
AC² = AB² + BC² - 2(AB × BC)CosAC
AC² = 60² + 180² - 2(60 × 180)Cos118
AC² = 3600 + 32400 - 21600Cos118
AC² = 36000 - 21600(-0.46947156)
AC² = 36000 + 10140.59
AC² = 46140.59
AC = √46140.59
AC = 215 m
Please help thank you
Answers
Answer:
D
Step-by-step explanation:
subsitute each of the x and y values for each of the equations and if they both equal each other It is correct.
Answer:
x = 2, y= -1
Step-by-step explanation:
12x - y = 25
9x + y = 17
add both equations to eliminate y
21x = 42
divide by 21
x = 42/21
x = 2
sub x in equation i to find y
12(2) - y = 25
24 - y = 25
-y = 1
therefore y = -1, x = 2
Convert 0.396 to a fraction in its simplest form
Answers
what is the solution to this inequality x/10+6≥8
Answers
Answer:
x ≥ 20
Step-by-step explanation:
First, we want to isolate x. We can start to do that by subtracting 6 to both sides.
x/10≥2
Now, we multiply each side by 10.
x ≥ 20
That's the answer, all values above or equal to 20 are solutions.
Answer:
The answer is x_> 20
Step-by-step explanation:
0.0995 rounded to 3 decimal places
Answers
Answer:
0.100
Step-by-step explanation:
0.0995 has 4 decimal places
5>4 so round up
9 turns to 10, the 1 is "added on" to the number ahead
9 turns to 10 again, the 1 is "added on" to the number ahead
0 turns to 1
you are left with 0.100
Answer:
0.100
Step-by-step explanation:
Three decimal places: 0. 0 / 9 / 9 / 5
Rounding number: 0. 0 / 9 / 9 / 5
Since it is 5, add 1 to the second 9. This will result to 0 while adding 1 to the first 9. Again, this would result to 10 which will add 1 to the next number, 0.
0.1000
Since the question wants you to round three places, you were not told to remove the zeros in those decimal places. So only remove the last 0.
0.100 is the answer
PLEASE HELP IMAGE ATTACHED!!
Answers
Answer:
Step-by-step explanation:
Parallel lines have same slope
19) y = x - 4
m = 1 ; (2, 3 )
Equation: y - y₁ = m(x- x₁)
y - 3 = 1(x - 2)
y - 3 = x -2
y = x - 2 + 3
y = x + 1
20) 2x + 3y = 3
We have to write in y = mx + b form
3y = - 2x - 3
[tex]y=\frac{-2}{3}x-\frac{3}{3}\\\\y=\frac{-2}{3}x-1\\\\m=\frac{-2}{3}[/tex]; (-6, -1)
[tex]y-[-1]=\frac{-2}{3}(x-[-6])\\\\y+1=\frac{-2}{3}(x+6)\\\\y+1=\frac{-2}{3}x+\frac{-2}{3}*6\\\\y+1=\frac{-2}{3}x-4\\\\y=\frac{-2}{3}x-4-1\\\\y=\frac{-2}{3}x-5[/tex]
for perpendicular lines, m2 = -1/m1
21) y = 2x+ 5
m1 = 2
[tex]m_{2}=\frac{-1}{2}[/tex]; (-2,8)
[tex]y-8=\frac{-1}{2}(x-[-2])\\\\y-8=\frac{-1}{2}(x+2)\\\\y-8=\frac{-1}{2}x+2*\frac{-1}{2}\\\\y-8=\frac{-1}{2}x-1\\\\y=\frac{-1}{2}x-1+8\\\\y=\frac{-1}{2}x+7[/tex]
22) x+ 4y = 8
4y = -x + 8
[tex]y=\frac{-1}{4}x+\frac{8}{4}\\\\y=\frac{-1}{4}x+2\\\\m_1=\frac{-1}{4}\\\\m_{2}=4\\\\[/tex]
m2 = 4; (-2,-11)
y - [-11] = 4(x -[-2])
y + 11 = 4 (x + 2)
y + 11 = 4x + 8
y = 4x + 8 - 11
y = 4x - 3
write h(x)=x2-6x + 3 in vertex form
Answers
Answer: The vertex form is h(x)=(x-3)^2-6
Step-by-step explanation:
Using the complete the square method, first complete any squares
X^2-6x+(-3)^2-(-3)^2+3
Use the binomial formula
(x-3)^2 - (-3)^2 +3
Simplify
(x-3)^2-6
Change each algebraic expression to a verbal expression.
1. A+B = 10
2. 4x - y = a
Answers
Answer:
1. A letter, A, added to a letter, B, equals ten.
2. A letter, x, which is multiplied by 4, then has a number, y, subtracted from it to equal a letter, a.
If you try write these out, I'm sure you'd get the algebraic expression given.
can someone help please
Answers
Answer:
11/8 or, 1 and 3/8
Step-by-step explanation:
First, we have to make both the denominators the same. In this case, we can multiply 3/4 by 2, to make 4, the denominator, into 8. What we do to the denominator, we must do to the numerator! So, we multiply 3 by 2, and get 6!
Now we have, 5/8 + 6/8, which equals 11/8! Which can also be simplified to 1 and 3/8 (because the numerator is larger than the denominator)
Hope this helps! :)
The congruence theorem that can be used to prove △LON ≅ △LMN is SSS. ASA. SAS. HL.
Answers
Answer:
The correct option is SSS (Side-Side-Side) Theorem
Step-by-step explanation:
The question is incomplete because the diagrams of ΔLON and ΔLMN are not given. I have attached the diagram of both triangles below for better understanding of the question.
Consider the diagram attached below. We have to find the congruence theorem which can be used to prove that ΔLON ≅ ΔLMN
We can see in the diagram that both triangle have a common side that is LN. It means 1 side of both triangles is congruent because LN≅LN
Consider the sides ON and MN. Both side have a single bar on them, which means that it is given that both of these side are congruent. Hence ON≅MN
Consider the sides LO and LM. Both side have a double bars on them, which means that it is given that both of these side are also congruent. Hence LO≅LM
SSS theorem states that if all sides of the triangles are congruent, then the triangles themselves are also congruent, which is the same case in this question
Answer:
D. SSS
Step-by-step explanation:
I hope this helps.
A fair dice is rolled 3 times in a row. The outcomes are shown below. Calculate the probability of all three events occurring. Roll Outcome 1st 5 2nd factor of 6 3rd more than 1
Answers
Answer:
5/54
Step-by-step explanation:
probability of the dice being 5 = 1/6
probability of the dice being a factor of 6 = 4/6
probability of the dice being more than 1 = 5/6
1/6 * 4/6 = 4/36
4/36 * 5/6 = 20/216
20/216 simplified to lowest is equal to 5/54
Which statements are true about the parabola represented by the equation y=−3x^2+18x+23 Select all that apply. 1. The leading coefficient is positive, so the parabola opens up. 2. The leading coefficient is negative, so the parabola opens down. 3. The parabola has a maximum. 4. The parabola has a minimum.
Answers
Answer:
2, 3
Step-by-step explanation:
2. The leading coefficient is -3. When the leading coefficient is negative, the parabola opens down.
3. When the parabola opens down, it has a maximum point, but no minimum point. (when the parabola opens up, it has a minimum, but no maximum)
I hope this helps :)
The right statements about equation y=−3x^2+18x+23 is 2) The leading coefficient is negative and 3) The parabola has a maximum.
What is a parabola?A parabola is a plane curve which is mirror-symmetrical and can be downward, upward, leftward and rightward shaped.
What are the statements?Second is true because when the coefficient is negative the parabola opens down because their values starts decreasing.
Third is true because when the parabola opens down it has a maximum point and no minimum point. On the other hand when the coefficient is positive it opens up.
Learn more about parabola at https://brainly.com/question/4148030
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PLEASE HELP I DONT KNOW WHAT TO DO !! I APPRECIATE IT IF YOU HELP ME !
Answers
Answer:
x = ±20
Step-by-step explanation:
x^2 -1=399
Add 1 to each side
x^2 = 399+1
x^2 = 400
Take the square root of each side
sqrt(x^2) = ±sqrt(400)
x = ±20
cereal is on sale for $3.60 for a 9-ounce box. what is the price per ounce?
Answers
Answer:
$0.40 per oz
Step-by-step explanation:
given that the cereal is $3.60 for a 9 oz box
i.e
9 oz ----> costs $3.60
1 oz ----> costs $3.60 ÷ 9 = $0.40
hence the unit rate is $0.40 per oz
Answer:
0.40 per ounce
Step-by-step explanation:
The question asks is to find the unit rate, or price per ounce.
To find this, we need to divide the price by the number of ounces.
price/ ounces
It costs $3.60 for 9 ounces of cereal.
$3.60/9 ounces
Divide $3.60 by 9 (3.60/9=0.4)
$0.4/ounce
It costs $0.40 per ounce of cereal.
if four points are collinear, they are also coplanar
Answers
Answer:
Hi there!
The correct answer is: True
Step-by-step explanation:
If there is a line, there are infinite planes that pass through that line, therefore since the 4 points are in a line, they are coplanar .
An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated. (a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw (b) Use the possibility diagram to calculate the probability that the product of the two numbers is (i) A prime number (ii) Not a perfect square (iii) A multiple of 5 (iv) Less than or equal to 21 (v) Divisible by 4 or 6
Answers
Answer:
this question is roung
Multiply 17/18 by the reciprocal of -289/324.
Answers
Answer:
18/17
Step-by-step explanation:
the negative reciprocal of -289/324 is 324/289. When it is multiplied by 17/18 you get 18/17 as the answer.
Answer:
[tex] - 1 \frac{1}{17}[/tex]
Step-by-step explanation:
[tex]Reciprocal \: of \: - \frac{289}{324} = - \frac{324}{289} \\ \\ \frac{17}{18} \times (- \frac{324}{289} ) \\ \\ = \frac{17}{18} \times (- \frac{18 \times 18}{17 \times 17} ) \\ \\ = - \frac{18}{17} \\ \\ = - 1 \frac{1}{17} \\ [/tex]
select a brand with the least expensive corn per ounce
A) ounces price
18 1.50
36 3.00
54 4.50
B) .75 for 15 oz
C) Maia buys an 11 ounce can of brand c corn for 2.20
Answers
Answer: Option B.
Step-by-step explanation:
The price per ounce can be calculated as the amount of you paid divided the number of ounces that you get.
A) we have a table:
ounces price
18 $1.5
36 $3.00
54 $4.5
We can see that here we have a linear relationship. for example, the price for 18 ounces is $1.5
Then the price per ounce is:
p = $1.5/18 = $0.083
B) here we know that 15 oz cost $0.75, the price per ounce is:
p = $0.75/15 = $0.05
C) here we have 11 ounces, and the price is $2.20
then we have:
p = $2.2/11 = $0.2
Then we can conclude that the least expensive is option B.
Answer:b
Step-by-step explanation:
did it on khan